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This research advances the construction of quantum locally recoverable codes by leveraging BCH and homothetic-BCH structures to achieve optimality within distributed storage systems. The updated version expands realizable parameters for multiple erasure correction, directly addressing scalability challenges in large-scale cloud infrastructure relying on quantum error mitigation techniques.

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Quantum $(r,\delta)$-Locally Recoverable BCH and Homothetic-BCH Codes

arXiv28 iulie 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2601.22567v2 Announce Type: replace-cross Abstract: Quantum $(r,\delta)$-locally recoverable codes ($(r,\delta)$-LRCs) are the quantum version of classical $(r,\delta)$-LRCs designed to recover multiple failures in large-scale distributed and cloud storage systems. A quantum $(r,\delta)$-LRC, $Q(C)$, can be constructed from an $(r,\delta)$-LRC, $C$, which is Euclidean or Hermitian dual-containing. This article is devoted to studying how to get quantum $(r,\delta)$-LRCs from BCH and homothetic-BCH codes. As a consequence, we give pure quantum $(r,\delta)$-LRCs which are optimal for the Singleton-like bound.

Abstract:Quantum $(r,\delta)$-locally recoverable codes ($(r,\delta)$-LRCs) are the quantum version of classical $(r,\delta)$-LRCs designed to recover multiple failures in large-scale distributed and cloud storage systems. A quantum $(r,\delta)$-LRC, $Q(C)$, can be constructed from an $(r,\delta)$-LRC, $C$, which is Euclidean or Hermitian dual-containing. This article is devoted to studying how to get quantum $(r,\delta)$-LRCs from BCH and homothetic-BCH codes. As a consequence, we give pure quantum $(r,\delta)$-LRCs which are optimal for the Singleton-like bound.

24 pages, 6 tables. Version 2 improves the code construction and expands the set of realizable parameters. It also adds comprehensive tables comparing realizable parameters with those known to the authors from previous literature on multiple erasure correction as of July 2026

Information Theory (cs.IT); Quantum Physics (quant-ph)

arXiv:2601.22567 [cs.IT]

(or arXiv:2601.22567v2 [cs.IT] for this version)

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